A path integral formulation for particle detectors: the Unruh-DeWitt model as a line defect

Particle detectors are an ubiquitous tool for probing quantum fields in the context of relativistic information (RQI). We formulate Unruh-DeWitt (UDW) particle detector model terms path integral formalism. The formulation is able to recover results general globally hyperbolic spacetimes and arbitrary trajectories. Integrating out detector's degrees freedom yields a line defect that allows one express transition probability Feynman diagrams. Inspired by light-matter interaction, we propose gauge invariant whose associated related derivative Wilson line. This another instance where nonlocal operators theories can be interpreted as physical probes fields.